SCREE: Scree Plot

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Scree Plot

Description

The scree plot was originally introduced by Cattell (1966) to perform the scree test. In a scree plot, the eigenvalues of the factors / components are plotted against the index of the factors / components, ordered from 1 to N factors components, hence from largest to smallest eigenvalue. According to the scree test, the number of factors / components to retain is the number of factors / components to the left of the "elbow" (where the curve starts to level off) in the scree plot.

Usage

SCREE(
  x,
  eigen_type = c("PCA", "SMC", "EFA"),
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall"),
  n_factors = 1,
  ...
)

Arguments

x	data.frame or matrix. Dataframe or matrix of raw data or matrix with correlations.
eigen_type	character. On what the eigenvalues should be found. Can be either "PCA", "SMC", or "EFA", or some combination of them. If using "PCA", the diagonal values of the correlation matrices are left to be 1. If using "SMC", the diagonal of the correlation matrices is replaced by the squared multiple correlations (SMCs) of the indicators. If using "EFA", eigenvalues are found on the correlation matrices with the final communalities of an exploratory factor analysis solution (default is principal axis factoring extracting 1 factor) as diagonal.
use	character. Passed to stats::cor if raw data is given as input. Default is "pairwise.complete.obs".
cor_method	character. Passed to stats::cor. Default is "pearson".
n_factors	numeric. Number of factors to extract if "EFA" is included in eigen_type. Default is 1.
...	Additional arguments passed to EFA. For example, to change the extraction method (PAF is default).

Details

As the scree test requires visual examination, the test has been especially criticized for its subjectivity and with this low inter-rater reliability. Moreover, a scree plot can be ambiguous if there are either no clear "elbow" or multiple "elbows", making it difficult to judge just where the eigenvalues do level off. Finally, the scree test has also been found to be less accurate than other factor retention criteria. For all these reasons, the scree test has been recommended against, at least for exclusive use as a factor retention criterion (Zwick & Velicer, 1986)

The SCREE function can also be called together with other factor retention criteria in the N_FACTORS function.

Value

A list of class SCREE containing

eigen_PCA	A vector containing the eigenvalues found with PCA.
eigen_SMC	A vector containing the eigenvalues found with SMCs.
eigen_EFA	A vector containing the eigenvalues found with EFA.
settings	A list of the settings used.

Source

Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. https://doi.org/10.1207/s15327906mbr0102_10

Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442. http://dx.doi.org/10.1037/0033-2909.99.3.432

See Also

Other factor retention criteria: CD, EKC, HULL, PARALLEL, SMT

N_FACTORS as a wrapper function for this and all the above-mentioned factor retention criteria.

Examples

SCREE(test_models$baseline$cormat, eigen_type = c("PCA", "SMC"))

EFAtools documentation built on Jan. 6, 2023, 5:16 p.m.